Exchange interaction between ferromagnetic domain wall and electric current in very thin metallic films

TLDR

In very thin metallic films, a ferromagnetic domain wall behaves as a weak, smooth potential barrier (~10⁻² eV) due to s‑d exchange, with anisotropic s‑d exchange also contributing. The authors model the wall’s potential energy from the small misalignment of 4s conduction electron spins with the local s‑d exchange field, incorporating interband scattering by impurities or phonons and mutual electrostatic shielding between bands. They solve the electron transport equations, finding that the electron density varies slightly across the wall and that the resulting drive force per unit area, F≈2Ms μi⁻¹(ve−vw), is governed by the intrinsic wall mobility μi and should dominate over hydromagnetic drag in films thinner than ~0.1 µm.

Abstract

Since the wall thickness is at least 102 electron wavelengths, a domain wall acts, through the s-d exchange interaction, like a very weak and smooth potential barrier of height ≂10−2 eV, which does not reflect conduction electrons appreciably. The potential energy arises from the 4s conduction electron spin making a small angle with the local s-d exchange field. Anisotropic s-d exchange may also contribute to the potential barrier. A solution of the electron transport equations in the wall is obtained. In order for an electron current crossing the wall to exert an appreciable drive force on it, nonzero interband electron scattering by impurities or phonons is needed. The electron density for a given band varies slightly with location inside the wall, and depends on the current. Mutual electrostatic shielding between bands is taken into account. The drive force per unit wall area is F≂2Ms μ−1i (ve −vw), where ve and vw are electron drift speed and wall speed. In other words, this drive force at ve ≠0 is governed by the same intrinsic wall mobility μi as the well-known intrinsic wall damping force at vw ≠0. While hydromagnetic ‘‘domain drag’’ forces associated with the Hall effect are dominant in samples of usual thickness, this ‘‘exchange domain drag’’ force is expected to dominate in films thinner than ≂0.1 μm.